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We introduce Deep-CEE (Deep Learning for Galaxy Cluster Extraction and Evaluation), a proof of concept for a novel deep learning technique, applied directly to wide-field colour imaging to search for galaxy clusters, without the need for photometric catalogues. This technique is complementary to traditional methods and could also be used in combination with them to confirm galaxy cluster candidates. We use a state-of-the-art probabilistic algorithm, adapted to localize and classify galaxy clusters from other astronomical objects in SDSS imaging. As there is an abundance of labelled data for galaxy clusters from previous classifications in publicly available catalogues, we do not need to rely on simulated data. This means we keep our training data as realistic as possible, which is advantageous when training a deep learning algorithm. Ultimately, we will apply our model to surveys such as LSST and Euclid to probe wider and deeper into unexplored regions of the Universe. This will produce large samples of both high redshift and low mass clusters, which can be utilized to constrain both environment-driven galaxy evolution and cosmology.
Convolutional Networks (ConvNets) have recently improved image recognition performance thanks to end-to-end learning of deep feed-forward models from raw pixels. Deep learning is a marked departure from the previous state of the art, the Fisher Vector (FV), which relied on gradient-based encoding of local hand-crafted features. In this paper, we discuss a novel connection between these two approaches. First, we show that one can derive gradient representations from ConvNets in a similar fashion to the FV. Second, we show that this gradient representation actually corresponds to a structured matrix that allows for efficient similarity computation. We experimentally study the benefits of transferring this representation over the outputs of ConvNet layers, and find consistent improvements on the Pascal VOC 2007 and 2012 datasets.
Deep Convolutional Neural Networks (DCNNs) is currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose $Pi$-Nets, a new class of DCNNs. $Pi$-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. $Pi$-Nets can be implemented using special kind of skip connections and their parameters can be represented via high-order tensors. We empirically demonstrate that $Pi$-Nets have better representation power than standard DCNNs and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, $Pi$-Nets produce state-of-the-art results in challenging tasks, such as image generation. Lastly, our framework elucidates why recent generative models, such as StyleGAN, improve upon their predecessors, e.g., ProGAN.
We present a new deep spectroscopic catalogue for Abell 85, within 3.0 $times$ 2.6 Mpc$^2$ and down to $M_{r} sim M_{r}^* +6$. Using the Visible Multi-Object Spectrograph at the Very Large Telescope (VIMOS@VLT) and the AutoFiber 2 at the William Herschel Telescope (AF2@WHT), we obtained almost 1,430 new redshifts for galaxies with $m_r leq 21$ mag and $langle mu_{e,r} rangle leq 24$ mag arcsec$^{-2}$. These redshifts, together with SDSS-DR6 and NED spectroscopic information, result in 460 confirmed cluster members. This dataset allows the study of the luminosity function (LF) of the cluster galaxies covering three orders of magnitudes in luminosities. The total and radial LFs are best modelled by a double Schechter function. The normalized LFs show that their bright ($M_{r} leq -21.5$) and faint ($M_{r}geq -18.0$) ends are independent of clustercentric distance and similar to the field LFs unlike the intermediate luminosity range ($-21.5 leq M_{r} leq -18.0$). Similar results are found for the LFs of the dominant types of galaxies: red, passive, virialized and early-infall members. On the contrary, the LFs of blue, star forming, non-virialized and recent-infall galaxies are well described by a single Schechter function. These populations contribute to a small fraction of the galaxy density in the innermost cluster region. However, in the outskirts of the cluster, they have similar densities to red, passive, virialized and early-infall members at the LF faint end. These results confirm a clear dependence of the colour and star formation of Abell 85 members in the cluster centric distance.
The next generation of data-intensive surveys are bound to produce a vast amount of data, which can be dealt with using machine-learning methods to explore possible correlations within the multi-dimensional parameter space. We explore the classification capabilities of convolution neural networks (CNNs) to identify galaxy cluster members (CLMs) by using Hubble Space Telescope (HST) images of 15 galaxy clusters at redshift 0.19<z<0.60, observed as part of the CLASH and Hubble Frontier Field programmes. We used extensive spectroscopic information, based on the CLASH-VLT VIMOS programme combined with MUSE observations, to define the knowledge base. We performed various tests to quantify how well CNNs can identify cluster members on the basis of imaging information only. We investigated the CNN capability to predict source memberships outside the training coverage, by identifying CLMs at the faint end of the magnitude distributions. We find that the CNNs achieve a purity-completeness rate ~90%, demonstrating stable behaviour, along with a remarkable generalisation capability with respect to cluster redshifts. We concluded that if extensive spectroscopic information is available as a training base, the proposed approach is a valid alternative to catalogue-based methods because it has the advantage of avoiding photometric measurements, which are particularly challenging and time-consuming in crowded cluster cores. As a byproduct, we identified 372 photometric CLMs, with mag(F814)<25, to complete the sample of 812 spectroscopic CLMs in four galaxy clusters RX~J2248-4431, MACS~J0416-2403, MACS~J1206-0847 and MACS~J1149+2223. When this technique is applied to the data that are expected to become available from forthcoming surveys, it will be an efficient tool for a variety of studies requiring CLM selection, such as galaxy number densities, luminosity functions, and lensing mass reconstruction.
We present a morphological catalogue for $sim$ 670,000 galaxies in the Sloan Digital Sky Survey in two flavours: T-Type, related to the Hubble sequence, and Galaxy Zoo 2 (GZ2 hereafter) classification scheme. By combining accurate existing visual classification catalogues with machine learning, we provide the largest and most accurate morphological catalogue up to date. The classifications are obtained with Deep Learning algorithms using Convolutional Neural Networks (CNNs). We use two visual classification catalogues, GZ2 and Nair & Abraham (2010), for training CNNs with colour images in order to obtain T-Types and a series of GZ2 type questions (disk/features, edge-on galaxies, bar signature, bulge prominence, roundness and mergers). We also provide an additional probability enabling a separation between pure elliptical (E) from S0, where the T-Type model is not so efficient. For the T-Type, our results show smaller offset and scatter than previous models trained with support vector machines. For the GZ2 type questions, our models have large accuracy (> 97%), precision and recall values (> 90%) when applied to a test sample with the same characteristics as the one used for training. The catalogue is publicly released with the paper.